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Point Q is plotted on the coordinate grid. Point P is at (40, −20). Point R is vertically above point Q. It is at the same distance from point Q as point P is from point Q. Which of these shows the coordinates of point R and its distance from point Q?

Point Q is plotted on the coordinate grid. Point P is at (40, −20). Point R is vertically-example-1
User Arvie
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1 Answer

6 votes

Answer:


\displaystyle d_(RP)=50√(2)\ units

Explanation:

Distance between points in
R^2

If P(p1,p2) and Q(q1,q2) are points on the plane
R^2, the distance between them is


\displaystyle d=√((q_1-p_1)^2+(q_2-p_2)^2)

We have Q(-10,-20) plotted on the coordinate grid. We also know that P is at (40, -20). We can see they have the same y-coordinate, so the distance between them is computed simply by subtracting their x-coordinates


\displaystyle d_(PQ)=40-(-10)=50

We must locate R knowing it's vertically above Q (x-coordinate = -10) and at the same distance from point Q as point P is from point Q. That means that from R to Q there are 50 units. They-coordinate of R will be -20+50=30.

The point R is located at (-10,30)

The distance from R to P is


\displaystyle d_(RP)=√((-10-40)^2+(30+20)^2)


\displaystyle d_(RP)=√((-50)^2+50^2)


\displaystyle d_(RP)=√(2500+2500)


\displaystyle d_(RP)=√(5000)


\displaystyle d_(RP)=50√(2)\ units

User CommandZ
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